A long-standing conjecture in macroeconomics is that recent declines in exchange rate pass-through are in part due to improved monetary policy performance. In a large sample of emerging and advanced economies, we find evidence of a strong link between exchange rate pass-through to consumer prices and the monetary policy regime's performance in delivering price stability. Using input-output tables, we decompose exchange rate pass-through to consumer prices into a component that reflects the adjustment of imported goods at the border, and another that captures the response of all other prices. We find that price stability and central bank credibility have reduced the second component.